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Topic: Science
Number of pages / Number of words: 5 / 1195
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a ranking of A > B > C implies that ?A? is preferred to ?B?, ?B? is preferred to ?C? and, transitively, ?A? is preferred to ?C?):

1. A > B > C

2. A > C > B

3. B > A > C

4. B > C > A

5. C > A > B

6. C > B > A

From this, it is seen that in general, there are there are ?n!? ways a voter could prefer ?n? candidates...


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Now a voting vector is a vector whose components say how much it?s worth to be ranked first, second, third, etc. Each candidate would have a vector whose ith component would be how many times that candidate was ranked ith by a voter. In these elections, the winner is the candidate who has the highest dot product with the voting vector...


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